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Automatically Merging Ajacent Rectangles

I've been making a top-down shooter game in XNA that requires rectangular collision for the map.
The collision walls for a map is stored in a text file in the format of:rect[0,0,1024,8]
The values correspond to defining a rectangle (x, y, width, height).
I've been thinking that I could write a separate application that can illiterate through the data of the map image, find out the pixels that are black (or any color of the wall) and make rectangles there. Basically, this program will generate the rectangles required for the collision. Ideally, it would be pixel perfect, which would require something like a thousand rectangles each 1 pixel wide that covers all the walls.
Is there a possible way to detect which of these rectangles (or squares I should say) are adjacent to one another, then connect them into the a bigger (but still covering the same area) rectangle?
EG. Lets say I have a wall that is 10 by 2. The program would generate 20 different rectangles, each 1 pixel high. How would I efficiently detect that these rectangles are adjacent and automatically make a 10 by 2 rectangle covering the whole wall instead of having 20 different little pixel rectangles?
EDIT: I've worked out a solution that fits my purposes, for future reference, my code is below:
//map is a bitmap, horizontalCollisions and collisions are List<Rectangle>s
for (int y = 0; y < map.Height; y++) //loop through pixels
{
for (int x = 0; x < map.Width; x++)
{
if (map.GetPixel(x, y).Name == "ff000000") //wall color
{
int i = 1;
while (map.GetPixel(x + i, y).Name == "ff000000")
{
if (i != map.Width - x)
{
i++;
}
if (i == map.Width - x)
{
break;
}
}
Rectangle r = new Rectangle(x, y, i, 1);//create and add
x += i - 1;
horizontalCollisions.Add(r);
}
}
}
for (int j = 0; j < horizontalCollisions.Count; j++)
{
int i = 1;
Rectangle current = horizontalCollisions[j];
Rectangle r = new Rectangle(current.X, current.Y + 1, current.Width, 1);
while(horizontalCollisions.Contains(r))
{
i++;
horizontalCollisions.Remove(r);
r = new Rectangle(current.X, current.Y + i, current.Width, 1);
}
Rectangle add = new Rectangle(current.X, current.Y, current.Width, i);
collisions.Add(add);
}
//collisions now has all the rectangles
Basically, it will loop through the pixel data horizontally. When it encounters a wall pixel, it will stop the counter and (using a while loop) move the counter towards the right, one by one until it hits a non-wall pixel. Then, it will create a rectangle of that width, and continue on. After this process, there will be a big list of rectangles, each 1px tall. Basically, a bunch of horizontal lines. The next loop will run through the horizontal lines, and using the same process as above, it will find out of there are any rectangles with the same X value and the same Width value under it (y+1). This will keep incrementing until there are none, in which one big rectangle will be created, and the used rectangles are deleted from the List. The final resulting list contains all the rectangles that will make up all the black pixels on the image (pretty efficiently, I think).

Etiquette may suggest that I should comment this instead of add it as an answer, but I do not yet have that capability, so bear with me.
I'm afraid I am not able to translate this into code for you, but I can send you towards some academic papers that discuss algorithms that can do some of the things that you're asking.
Other time this questions has appeared:
Find the set of largest contiguous rectangles to cover multiple areas
Puzzle: Find largest rectangle (maximal rectangle problem)
Papers linked in those questions:
Fast Algorithms To Partition Simple Rectilinear Polygons
Polygon Decomposition
The Maximal Rectangle Problem
Hopefully these questions and papers can lead help you find the answer you're looking for, or at least scare you off towards finding another solution.

find the center point of coordinate 2d array c#

Is there a formula to average all the x, y coordinates and find the location in the dead center of them.
I have 100x100 squares and inside them are large clumps of 1x1 red and black points, I want to determine out of the red points which one is in the middle.
I looked into line of best fit formulas but I am not sure if this is what I need.
Sometimes all the red will be on one side, or the other side. I want to essentially draw a line then find the center point of that line, or just find the center point of the red squares only. based on the 100x100 grid.

List<Point> dots = new List<Point>();
int totalX = 0, totalY = 0;
foreach (Point p in dots)
{
totalX += p.X;
totalY += p.Y;
}
int centerX = totalX / dots.Count;
int centerY = totalY / dots.Count;

Simply average separately the x coordinates and the y coordinates, the result will be the coordinates of the "center".

What if there are two or more subsets of red points ? Do you want the black point inside them?
Otherwis, if I understood your question, just give a weight of 1 to red points and 0 to blacks. Then do the weighted mean on X and Y coordinate

Is there an efficient algorithm for segmentation of handwritten text?

I want to automatically divide an image of ancient handwritten text by lines (and by words in future).
The first obvious part is preprocessing the image...
I'm just using a simple digitization (based on brightness of pixel). After that I store data into two-dimensional array.
The next obvious part is analyzing the binary array.
My first algorithm was pretty simple - if there are more black pixels in a row of the array than the root-mean-square of Maximum and Minimum value, then this row is part of line.
After forming the list of lines I cut off lines with height that is less than average.
Finally it turned out into some kind of linear regression, trying to minimize the difference between the blank rows and text rows. (I assumed that fact)
My second attempt - I tried to use GA with several fitness functions.
The chromosome contained 3 values - xo, x1, x2. xo [-1;0] x1 [0;0.5] x2 [0;0.5]
Function, that determines identity the row to line is (xo + α1 x1 + α2 x2) > 0, where α1 is scaled sum of black pixels in row, α2 is median value of ranges between the extreme black pixels in row. (a1,a2 [0,1])
Another functions, that I tried is (x1 < α1 OR x2 > α2) and (1/xo + [a1 x1] / [a2 x2] ) > 0
The last function is the most efficient.
The fitness function is
(1 / (HeigthRange + SpacesRange)
Where range is difference between maximum and minimum. It represents the homogeneity of text. The global optimum of this function - the most smooth way to divide the image into lines.
I am using C# with my self-coded GA (classical, with 2-point crossover, gray-code chromosomes, maximum population is 40, mutation rate is 0.05)
Now I ran out of ideas how to divide this image into lines with ~100% accuracy.
What is the efficient algorithm to do this?
UPDATE:
Original BMP (1.3 MB)
UPDATE2:
Improved results on this text to 100%
How I did it:
fixed minor bug in range count
changed fitness function to 1/(distancesRange+1)*(heightsRange+1))
minimized classifying function to (1/xo + x2/range) > 0 (points in row now don't affect classification)
(i.e. optimized input data and made fitness function optimizations more explicit)
Problem:
GA surprisingly failed to recognize this line. I looked at debug data of 'find rages' function and found, that there is too much noise in 'unrecognized' place.
The function code is below:
public double[] Ranges()
{
var ranges = new double[_original.Height];
for (int y = 0; y < _original.Height; y++ )
{
ranges[y] = 0;
var dx = new List<int>();
int last = 0;
int x = 0;
while (last == 0 && x<_original.Width)
{
if (_bit[x, y])
last = x;
x++;
}
if (last == 0)
{
ranges[y] = 0;
continue;
}
for (x = last; x<_original.Width; x++)
{
if (!_bit[x, y]) continue;
if (last != x - 1)
{
dx.Add((x-last)+1);
}
last = x;
}
if (dx.Count > 2)
{
dx.Sort();
ranges[y] = dx[dx.Count / 2];
//ranges[y] = dx.Average();
}
else
ranges[y] = 0;
}
var maximum = ranges.Max();
for (int i = 0; i < ranges.Length; i++)
{
if (Math.Abs(ranges[i] - 0) < 0.9)
ranges[i] = maximum;
}
return ranges;
}
I'm using some hacks in this code. The main reason - I want to minimize the range between nearest black pixels, but if there are no pixels, the value becomes '0', and it becomes impossible to solve this problem with finding optimas. The second reason - this code is changing too frequently.
I'll try to fully change this code, but I have no idea how to do it.
Q:
If there is more efficient fitness function?
How to find more versatile determination function?

Although I'm not sure how to translate the following algorithm into GA (and I'm not sure why you need to use GA for this problem), and I could be off base in proposing it, here goes.
The simple technique I would propose is to count the number of black pixels per row. (Actually it's the dark pixel density per row.) This requires very few operations, and with a few additional calculations it's not difficult to find peaks in the pixel-sum histogram.
A raw histogram will look something like this, where the profile along the left side shows the number of dark pixels in a row. For visibility, the actual count is normalized to stretch out to x = 200.
After some additional, simple processing is added (described below), we can generate a histogram like this that can be clipped at some threshold value. What remains are peaks indicating the center of lines of text.
From there it's a simple matter to find the lines: just clip (threshold) the histogram at some value such as 1/2 or 2/3 the maximum, and optionally check that the width of the peak at your clipping threshold is some minimum value w.
One implementation of the full (yet still simple!) algorithm to find the nicer histogram is as follows:
Binarize the image using a "moving average" threshold or similar local thresholding technique in case a standard Otsu threshold operating on pixels near edges isn't satisfactory. Or, if you have a nice black-on-white image, just use 128 as your binarization threshold.
Create an array to store your histogram. This array's length will be the height of the image.
For each pixel (x,y) in the binarized image, find the number of dark pixels above and below (x,y) at some radius R. That is, count the number of dark pixels from (x, y - R) to x (y + R), inclusive.
If the number of dark pixels within a vertical radius R is equal or greater to R--that is, at least half the pixels are dark--then pixel (x,y) has sufficient vertical dark neighbors. Increment your bin count for row y.
As you march along each row, track the leftmost and rightmost x-values for pixels with sufficient neighbors. As long as the width (right - left + 1) exceeds some minimum value, divide the total count of dark pixels by this width. This normalizes the count to ensure the short lines like the very last line of text are included.
(Optional) Smooth the resulting histogram. I just used the mean over 3 rows.
The "vertical count" (step 3) eliminates horizontal strokes that happen to be located above or below the center line of text. A more sophisticated algorithm would just check directly above and below (x,y), but also to the upper left, upper right, lower left, and lower right.
With my rather crude implementation in C# I was able to process the image in less than 75 milliseconds. In C++, and with some basic optimization, I've little doubt the time could be cut down considerably.
This histogram method assumes the text is horizontal. Since the algorithm is reasonably fast, you may have enough time to calculate pixel count histograms at increments of every 5 degrees from the horizontal. The scan orientation with the greatest peak/valley differences would indicate the rotation.
I'm not familiar with GA terminology, but if what I've suggested is of some value I'm sure you can translate it into GA terms. In any case, I was interested in this problem anyway, so I might as well share.
EDIT: maybe for use GA, it's better to think in terms of "distance since previous dark pixel in X" (or along angle theta) and "distance since previous dark pixel in Y" (or along angle [theta - pi/2]). You might also check distance from white pixel to dark pixel in all radial directions (to find loops).
byte[,] arr = get2DArrayFromBitamp(); //source array from originalBitmap
int w = arr.GetLength(0); //width of 2D array
int h = arr.GetLength(1); //height of 2D array
//we can use a second 2D array of dark pixels that belong to vertical strokes
byte[,] bytes = new byte[w, h]; //dark pixels in vertical strokes
//initial morph
int r = 4; //radius to check for dark pixels
int count = 0; //number of dark pixels within radius
//fill the bytes[,] array only with pixels belonging to vertical strokes
for (int x = 0; x < w; x++)
{
//for the first r rows, just set pixels to white
for (int y = 0; y < r; y++)
{
bytes[x, y] = 255;
}
//assume pixels of value < 128 are dark pixels in text
for (int y = r; y < h - r - 1; y++)
{
count = 0;
//count the dark pixels above and below (x,y)
//total range of check is 2r, from -r to +r
for (int j = -r; j <= r; j++)
{
if (arr[x, y + j] < 128) count++;
}
//if half the pixels are dark, [x,y] is part of vertical stroke
bytes[x, y] = count >= r ? (byte)0 : (byte)255;
}
//for the last r rows, just set pixels to white
for (int y = h - r - 1; y < h; y++)
{
bytes[x, y] = 255;
}
}
//count the number of valid dark pixels in each row
float max = 0;
float[] bins = new float[h]; //normalized "dark pixel strength" for all h rows
int left, right, width; //leftmost and rightmost dark pixels in row
bool dark = false; //tracking variable
for (int y = 0; y < h; y++)
{
//initialize values at beginning of loop iteration
left = 0;
right = 0;
width = 100;
for (int x = 0; x < w; x++)
{
//use value of 128 as threshold between light and dark
dark = bytes[x, y] < 128;
//increment bin if pixel is dark
bins[y] += dark ? 1 : 0;
//update leftmost and rightmost dark pixels
if (dark)
{
if (left == 0) left = x;
if (x > right) right = x;
}
}
width = right - left + 1;
//for bins with few pixels, treat them as empty
if (bins[y] < 10) bins[y] = 0;
//normalize value according to width
//divide bin count by width (leftmost to rightmost)
bins[y] /= width;
//calculate the maximum bin value so that bins can be scaled when drawn
if (bins[y] > max) max = bins[y];
}
//calculated the smoothed value of each bin i by averaging bin i-1, i, and i+1
float[] smooth = new float[bins.Length];
smooth[0] = bins[0];
smooth[smooth.Length - 1] = bins[bins.Length - 1];
for (int i = 1; i < bins.Length - 1; i++)
{
smooth[i] = (bins[i - 1] + bins[i] + bins[i + 1])/3;
}
//create a new bitmap based on the original bitmap, then draw bins on top
Bitmap bmp = new Bitmap(originalBitmap);
using (Graphics gr = Graphics.FromImage(bmp))
{
for (int y = 0; y < bins.Length; y++)
{
//scale each bin so that it is drawn 200 pixels wide from the left edge
float value = 200 * (float)smooth[y] / max;
gr.DrawLine(Pens.Red, new PointF(0, y), new PointF(value, y));
}
}
pictureBox1.Image = bmp;

After fiddling around this for a while I found that I simply need to count the number of crossings for each line, that is, a switch from white to black would count as one, and a switch from black to white would increment by one again. By highlighting each line with a count > 66 I got close to 100% accuracy, except for the bottom most line.
Of course, would not be robust to slightly rotated scanned documents. And there is this disadvantage of needing to determine the correct threshold.

IMHO with the image shown that would be so hard to do 100% perfectly.
My answer is to give you alternate idea's.
Idea 1:
Make your own version of ReCaptcha (to put on your very own pron site) - and make it a fun game.. "Like cut out a word (edges should all be white space - with some tolerance for overlapping chars on above and below lines)."
Idea 2:
This was a game we played as kids, the wire of a coat hanger was all bent in waves and connected to a buzzer and you had to navigate a wand with a ring in the end with the wire through it, across one side to the other without making the buzzer go off. Perhaps you could adapt this idea and make a mobile game where people trace out the lines without touching black text (with tolerance for overlapping chars)... when they can do a line they get points and get to new levels where you give them harder images..
Idea 3:
Research how google/recaptcha got around it
Idea 4:
Get the SDK for photoshop and master the functionality of it Extract Edges tool
Idea 5:
Stretch the image heaps on the Y Axis which should help, apply the algorithm, then reduce the location measurements and apply them on the normal sized image.

Get surrounding pixels in array

Hey. My maths isn't great so I'm hoping someone can help me with this. I have a 1D array of pixels (representing a 2d image). In order to access a specific pixel, I'm using this formula:
image.Pixels[row * imageWidth + col] = pixelColor;
This is working, but I would also like to include pixels around the selected pixel. What's the fastest way, without using pointers directly, to get a group of pixels around the selected pixel with a radius of r and set their values to pixelColor? I'm trying to create a paint-type app and would like to vary brush sizes, which would be dictated by the radius size.
Thanks for any help.

I don't know C# specifically, but something to the effect of this should do you
for (i=-r ; i< r ; i++) {
for (j=-(r - i); j<(r - i); j++) {
image.Pixels[(row+i)*imageWidth + (col+j)]=pixelColour;
}
}
Edit the above actually paints a diamond, i've given my first hack idea to do a proper circle below
for (i=-r ; i<r ; i++) {
for (j=-r; j<r; j++) {
if((i*i + j*j)<(r*r)){
image.Pixels[(row+i)*imageWidth + (col+j)]=pixelColour;
}
}
}

The simple slow way would be to step through the range of pixels in row +- r and col +- r, and calculate the distance from row and col is not greater than r. Distance from col,row is squareroot (difference in x squared + difference in y squared).
A slightly faster way is to compare the square of the radius to the difference in x squared + difference in y squared as they are comparable.
Still faster is Bresenham's circle algorithm,
Another article:
Bresenham's Line and Circle Algorithms
Once you have the distance from col for any row, you can fill the pixels from col - distance to col + distance, no need to calculate both. So you can get away with calculating only half the circle.

C# Moving through an image in a spiral motion?

I want to move through the pixels of an image, not by going line by line, column by column in the "normal" way. But begin at the center pixel and going outward in a spiral motion. But I'm not sure how to do this.
Any suggestions on how this can be done?

You can do this by using parametric functions, function for radius is r(t) = R, and x(t) = Rcos(t) and y(t)=Rsin(t).
Do you mean something like this?

It would be helpful to think about this in reverse.
For example, starting at the top left corner and moving in a clockwise direction you would move along the top row, then down the right hand side, along the bottom, and up the left edge to the pixel under the starting point.
Then move along the second row, and continue in a spiral.
Depending on the dimensions of the image you will end up with either a single column of pixels or a single row of pixels and will be moving either up/down or left/right.
From this finishing point you can then follow your steps backwards and process all the pixels as you need to.
To work out your starting position mathematically you would need to know the width/height of the image as well as which pixel you would like to end on and the direction you want to be travelling in when you get to the last pixel.

Something like this should do it:
int x = width / 2;
int y = height / 2;
int left = width * height;
int dir = 0;
int cnt = 1;
int len = 2;
int[] move = { 1, 0, -1, 0, 1 };
while (left > 0) {
if (x >= 0 && x < width && y >= 0 && y < height) {
// here you do something with the pixel at x,y
left--;
}
x += move[dir % 4];
y += move[(dir % 4) + 1];
if (--cnt == 0) {
cnt = len++ / 2;
dir++;
}
}
If the image is not square, the spiral will continue outside the coordinates of the image until the entire image has been covered. The condition in the if statement makes sure that only coordinates that are part of the image are processed.